I have two units of the same TV. One does not power up from standby (standby light is on), the other does. I switched the PSUs between them and the problem stayed on the same TV, so the PSU is okay (Megmeet MP116A rev 1.0. Photos on this thread).
I guess that means the problem is the logic board, which is a Cultraview CV181H-X-41C (a brief spec for the CV181H-X-40C here, the 41C is similar):

full size
Should I assume it's capacitors to blame?
The bunch of capacitors and inductors to the left are around TI TPA3110LD2 audio amp, so maybe unrelated.
The two near the middle are next to a panel voltage select jumper, two voltage regulators, and flash.
The two to the right are near the power input and two regulators.
The one near the VGA connector is next to an SG Micro SGM330A analog video switch.
What should I try?
I guess that means the problem is the logic board, which is a Cultraview CV181H-X-41C (a brief spec for the CV181H-X-40C here, the 41C is similar):

full size
Should I assume it's capacitors to blame?
The bunch of capacitors and inductors to the left are around TI TPA3110LD2 audio amp, so maybe unrelated.
The two near the middle are next to a panel voltage select jumper, two voltage regulators, and flash.
The two to the right are near the power input and two regulators.
The one near the VGA connector is next to an SG Micro SGM330A analog video switch.
What should I try?
Comment